Previous |  Up |  Next


3-D discrete system; discrete Fourier transform
A theoretically attractive and computationally fast algorithm is presented for the determination of the coefficients of the determinantal polynomial and the coefficients of the adjoint polynomial matrix of a given three-dimensional (3–D) state space model of Fornasini–Marchesini type. The algorithm uses the discrete Fourier transform (DFT) and can be easily implemented on a digital computer.
[1] Antoniou G. E., Glentis G. O. A., Varoufakis S. J., Karras D. A.: Transfer function determination of singular systems using the DFT. IEEE Trans. Circuits and Systems CAS-36 (1989), 1140–1142 DOI 10.1109/31.192429 | MR 1003246
[2] Bose N. K.: Applied Multidimensional Systems. Van Nostrand, Reinhold, 1982 MR 0652483 | Zbl 0574.93031
[3] Fornasini E., Marchesini E.: Doubly indexed dynamical systems: state space models and structural properties. Math. Systems Theory 12 (1978), 1, 59–72 DOI 10.1007/BF01776566 | MR 0510621 | Zbl 0392.93034
[4] Galkowski K.: State Space Realizations on $n$-D Systems. Monograph No. 76, Wroclaw Technical University, Wroclaw 1994
[5] Kaczorek T.: Two dimensional linear systems. (Lecture Notes in Control and Informations Sciences 68.) Springer–Verlag, Berlin 1985 MR 0870854 | Zbl 0904.00029
[7] Luo H., Lu W.-S., Antoniou A.: New algorithms for the derivation of the transfer-function matrices of 2-D state-space discrete systems. I: Fundamental theory and applications. IEEE Trans. Circuits and Systems CAS-44 (1997), 2, 112–119 Zbl 0873.93006
[8] Oppenheim A. V., Scheafer R. W.: Digital Signal Processing. Prentice–Hall, Englewood Cliffs, N. J. 1975
[9] al L. E. Paccagnella et: FFT calculation of a determinental polynomial. IEEE Trans. Automat. Control AC-21 (1976), 401 DOI 10.1109/TAC.1976.1101226
[10] Paraskevopoulos P. N., Varoufakis S. J., Antoniou G. E.: Minimal state space realization of 3–D systems. IEE Proceedings Part G 135 (1988), 65–70
[11] Yeung K. S., Kumbi F.: Symbolic matrix inversion with application to electronic circuits. IEEE Trans. Circuits and Systems CAS-35 (1988), 2, 235–239 DOI 10.1109/31.1727 | Zbl 0643.65013
Partner of
EuDML logo